Mathematics · important
Homogeneous system criterion for JEE
Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
Formula
For homogeneous system \(AX=O\): trivial solution always exists; non-trivial solution exists if \(\det(A)=0\). If \(\det(A)\ne 0\), only trivial solution exists.
Variables: \(O\): zero column matrix.
Conditions: For square homogeneous linear systems.
Existence of non-zero solutions in parameter problems.